Analysis of H/sub 2/ performance robustness with respect to disturbance model uncertainty

A method for evaluating the H/sub 2/ performance robustness of an LTI SISO feedback system with respect to parametric uncertainties in the disturbance model is developed. The disturbance is assumed to be colored noise obtained by passing standard white noise through a linear finite-dimensional filter with uncertain coefficients. The method is based on the converse of a spectral factorization problem. The main result obtained is an explicit formula for the output variance in terms of the uncertain parameters of the coloring filter. This result is illustrated on a ship roll stabilization problem.